Engineering Dynamics

by J. Kim Vandiver, David Gossard

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Description

This course covers the basics of engineering dynamics. After this course, students will be able to evaluate free and forced vibration of linear multi-degree of freedom models of mechanical systems and matrix eigenvalue problems.

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VideoLecture 1: History of Dynamics; Motion in Moving Reference Frames

Prof. Vandiver introduces key historical thinkers in the study of dynamics. He then derives equations of motion using Newton's laws, gives an introduction to kinematics using reference frames and vectors, and goes over motion in moving reference frames.

Prof. Vandiver goes over kinematics (describing the motion of particles and rigid bodies), Newton's three laws of motion, about action and reaction forces, the importance of an inertial reference frames, and the definition of center of mass.

Prof. Vandiver goes over an example problem of a block on a slope, the applications of Newton's 3rd law to rigid bodies, kinematics in rotating and translating reference frames, and the derivative of a rotating vector in cylindrical coordinates.

Prof. Vandiver goes over velocity and acceleration in a translating and rotating coordinate system using polar and cylindrical coordinates, angular momentum of a particle, torque, the Coriolis force, and the definition of normal and tangential coordinates.

VideoRecitation 2: Velocity and Acceleration in Translating and Rotating Frames

This recitation includes a concept review for the week and covers an amusement park ride problem with velocity in translating and rotating frames. The class also covers questions regarding planar motion problems.

VideoLecture 5: Impulse, Torque, & Angular Momentum for a System of Particles

Prof. Vandiver goes over the use of tangential and normal coordinates, a review of linear momentum and impulse, then the definition and derivation of the torque/angular momentum relationship with respect to moving points and rigid bodies.

Prof. Vandiver goes over the time rate of change of linear and angular momentum for a particle, conservation of angular momentum, work equalling the change in kinetic energy, external and internal structural torques, and axis of rotation.

Prof. Vandiver begins the lecture by discussing some concepts students had trouble with, then goes over free body diagrams and degrees of freedom with example problems (hockey puck, elevator, stick against wall), and finally discusses fictitious forces.

Prof. Vandiver discusses fictitious forces at length and goes over several problems: the spool problem, the elevator with a cable that breaks, and the cart carrying water on an incline. Finally, he does a rotating mass demonstration.

Prof. Vandiver first goes over the problem of a body on rollers with an internal rotating mass, then the definition of the mass moment of inertia as a summation, and finally moments and products of inertia.

This recitation includes a concept review for the week, problems with the axis of spin on and not on the principal axis, and a discussion on finding the derivative of a rotating vector. The class concludes with a review of the quiz.

Prof. Vandiver starts with a review of applicable physical laws; he then goes over an example Class 4 problem with moving points of constraint, the tipping box problem, an alternative form of Euler's equation, and ends with a question and answer period.

Prof. Vandiver goes over the concept questions for the week, the kinematic approach to finding generalized forces, the example of a wheel on moving cart with an incline, and the mass sliding on rod example.

Prof. Vandiver goes over various problems to review for the quiz, such as sticking and sliding in a circular track, a rotating T-bar with an imbalance, a pendulum in an elevator, and other pendulum problems.

VideoLecture 20: Linear System Modeling a Single Degree of Freedom Oscillator

Prof. Vandiver goes over the damped response of spring-mass-dashpot system to ICs, the ballistic pendulum example, experimental determination of damping ratio, steady state linear system response to harmonic input, and a beam with a rotating mass shaker.

Prof. Gossard goes over obtaining the equations of motion of a 2 DOF system, finding natural frequencies by the characteristic equation, finding mode shapes; he then demonstrates via Matlab simulation and a real 2 DOF system response to initial conditions.

Prof. Vandiver begins with an overview then goes over the linearization of a 2-DOF system, free vibration of linear multi-DOF systems, finding natural frequencies and mode shapes of multi-DOF systems, and mode superposition analysis of a 2-DOF system.

Prof. Vandiver goes over the use of Rayleigh damping to model modal damping ratios, steady state response to harmonic excitation by the method of modal analysis, the direct method for assembling the stiffness of an N DOF system.

VideoLecture 26: Response of 2-DOF Systems by the Use of Transfer Functions

Prof. Vandiver goes over analyzing the response of a 2-DOF system to harmonic excitation with transfer functions, using a dynamic absorber to mitigate problem vibration, and does a demonstration of a dynamic absorber using a strobe and a vibrating beam.

Prof. Vandiver goes over wave propagation on a long string, flow-induced vibration of long strings and beams, application of the wave equation to rods, organ pipes, shower stalls with demonstrations, and vibration of beams (dispersion in wave propagation).